Question

Find a degree 3 polynomial with real coefficients having zeros 2 and 3 i and a lead coefficient of 1. Write P in expanded form. Be sure to write the full equation, including P ( x ) = .

Answer 1

Rhe polynomial is P(x) = x³ -2x² + 9x - 18 if the zeros are 2 and 3i and a lead coefficient of 1

What is polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

$\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n$

We have:

The zeros of a polynomial are 2 and 3i and a lead coefficient of 1.

As we know, zeros of a polynomial are occurs in pairs

So the zeros are 2,3i,-3i

The factor form of a polynomial:

P(x) = (x- 2)(x - 3i)(x + 3i)

$\rm P(x) =\left(x-2\right)\left(x^2+\left(-3\right)^2\right)$

$\rm P(x) =\left(x-2\right)\left(x^2+9\right)$

$\rm P(x) =x^3+9x-2x^2-18$

Thus, the polynomial is P(x) = x³ -2x² + 9x - 18 if the zeros are 2 and 3i and a lead coefficient of 1

Learn more about polynomial here:

brainly.com/question/17822016

#SPJ1